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Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions
Published 7 Jul 2020 in math.NT and math.CO | (2007.03528v2)
Abstract: We show that if $A\subset {1,\ldots,N}$ contains no non-trivial three-term arithmetic progressions then $\lvert A\rvert \ll N/(\log N){1+c}$ for some absolute constant $c>0$. In particular, this proves the first non-trivial case of a conjecture of Erd\H{o}s on arithmetic progressions.
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